The misconception of the your/you’re construction is more common than you might think. This is because they are homophones in spoken English; we have no audible markers for differentiation. In written English, however, the distinction is clear—and more, it is very, very important.
“Your” is possessive. I sat in your chair. I gave you your coffee. I’m allergic to your cat. These sentences show that the person to whom you are talking owns something. He owns the chair. He owns the coffee. She owns the cat. The object that you are talking about is understood in reference to that ownership. Otherwise it would just be a chair, or a cup of coffee, or a cat.
In linguistics, we call this a modifier. A modifier adds more specification to the term, such as saying whose is the chair or the coffee or the cat. We use modifiers every day without thinking. Modifiers improve ease of conversation by removing ambiguity. In writing, this is especially important because we do not have the advantage of being able to explain an ambiguous utterance. Using “you’re” instead of the possessive “your” is confusing and unprofessional.
“You’re” is a contraction of “you are,” which does not modify nouns. Instead, it is a verb modifying the pronoun “you.” I will only go to the movie if you’re going. If you’re happy with the dog, then I am too.
One of the tricks I use when trying to figure out whether to use the possessive or the contraction is to insert “you are” into my sentence. This way, I can see if the sentence makes sense, or if I am trying to use the wrong word. “If you are happy with the cat, then I am too” is a proper sentence. The verb agrees with the pronoun, and all the nouns are accounted for. However, “I sat in you are chair” is nonsensical. Does it mean that the subject is a chair? Did the speaker sit on a chair, in a chair, on a person, in a person? It introduces ambiguity and also just sounds strange. A rule of thumb for copyeditors is whether or not It Just Looks Funny (IJLF). If it does look funny, try to figure out why. If it doesn’t, great! Writing is hard and even I need to go over things two or three times before I am satisfied.